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Business & Management - Operations Research & Decision Theory | Introduction to the Theory of Games - Concepts, Methods, Applications

Introduction to the Theory of Games

Concepts, Methods, Applications

Forgó, Ferenc, Szép, Jeno, Szidarovszky, Ferenc

1999, XII, 340 p.

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  • About this book

Game theory, defined in the broadest sense, is a collection of mathematical models designed for the analysis of strategic aspects of situations of conflict and cooperation in a broad spectrum of fields including economics, politics, biology, engineering, and operations research. This book, besides covering the classical results of game theory, places special emphasis on methods of determining `solutions' of various game models. Generalizations reaching beyond the `convexity paradigm' and leading to nonconvex optimization problems are enhanced and discussed in more detail than in standard texts on this subject. The development is theoretical-mathematical interspersed with elucidating interpretations and examples.
Audience: The material in the book is accessible to PhD and graduate students and will also be of interest to researchers. Solid knowledge of standard undergraduate mathematics is required to read the book.

Content Level » Research

Related subjects » Applications - Economic Theory - Operations Research & Decision Theory - Political Science

Table of contents 

Preface. Introduction. I: Noncooperative games. 1. Noncooperative games forms. 2. Nash equilibria. 3. Existence of Nash equilibrium. 4. Uniqueness of Nash equilibrium. 5. Mixed extensions of finite games. 6. Computation of equilibria in mixed extensions of finite games. 7. The oligopoly game. 8. Two-person zero-sum games. 9. Matrix games. 10. Games played over the unit hypercube. 11. Bimatrix games. 12. Repeated games. 13. Games with incomplete information. II: Cooperative games. 14. Games in characteristic function form. 15. The core. 16. Stable sets. 17. The nucleolus. 18. The Shapley value. 19. The kernel and the bargaining set. 20. Game theory and cost allocation. 21. Games without transferable utility. 22. The Nash bargaining solution and its extensions. 23. Two-person bargaining processes. Problems and exercises. Appendix. References. Index.

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